Instron Lab results

1. The problem statement, all variables and given/known data
Hi,
I'm having a little trouble understanding some of the results retrieved from my engineering mechanic's classes recent compression experiment with an Instron machine. Specifically when plotting the data retrieved from the machine we see a non linear region before the linear elastic region and have no idea what it represents only that we are told to ignore it when calculating the modulus of elasticity and resilience.

So the questions are..
a) What could have caused the initial non linear shallow gradient before the linearly elastic region?
b) Why didn't the samples expand uniformly instead of bulking?

3. The attempt at a solution
a) I'm honestly struggling to think of possible reasons for this.. could it have to do with the machine calibrating itself? For example, when setting up the machine, we set it such that the plate was very close to touching and then used the more sensitive control to position it such that it is only just touching. Or is it that the material deforms from lower stress initially until it reaches the linear elastic region? (if that at all made sense)
b) I'm lost for this one too, I can't even find reference to it in my materials textbook or online - to describe it by looking at it I guess I would call it 'reverse necking' or 'bulging', but I don't know what it's done that. My understanding is that with an evenly distributed load an object should deform uniformly - with that I would assume that the stress hasn't been distributed evenly.
Is it potentially from an uneven surface resultant from the material being cut? Material defects? Really need help with these two.. thanks!

If my answers appear silly or stupid, I apologise.. it only demonstrates my lack of understanding and need of help!